If points A and B are randomly placed on the circumference of a circle with radius 2, what is the probability that the length of chord AB is greater than 2?
A)1/4
B)1/3
C)1/2
D)2/3
E)3/4
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If points A and B are randomly placed
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theCodeToGMAT
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Hi guerrero,
First off, a "chord" is defined as a line that connects any two points on the circumference of a circle. The longest chord on any circle is the diameter of the circle, but any two points can form a cord.
To solve this question, try this....For this question, we have a radius of 2. Pick a point on the circumference. If you draw a cord with a length of 2 from that point, you can then draw two radii to those two points to form a triangle. What type of triangle has three sides that are all the same length? An equilateral triangle, which has angles of 60/60/60.
Now, from your starting point, draw another cord of length 2 in the other direction. You'll end up repeating the steps above and you'll end up with another 60/60/60 triangle.
Those two central angles: 60 + 60 = 120 degrees. Your starting point to every point OUTSIDE of that 120 degrees will create a cord that is GREATER than 2. So, 240 degrees of the circle will give you the result that you're looking for.
Final answer: [spoiler]240/360 = 2/3 = D[/spoiler]
GMAT assassins aren't born, they're made,
Rich
First off, a "chord" is defined as a line that connects any two points on the circumference of a circle. The longest chord on any circle is the diameter of the circle, but any two points can form a cord.
To solve this question, try this....For this question, we have a radius of 2. Pick a point on the circumference. If you draw a cord with a length of 2 from that point, you can then draw two radii to those two points to form a triangle. What type of triangle has three sides that are all the same length? An equilateral triangle, which has angles of 60/60/60.
Now, from your starting point, draw another cord of length 2 in the other direction. You'll end up repeating the steps above and you'll end up with another 60/60/60 triangle.
Those two central angles: 60 + 60 = 120 degrees. Your starting point to every point OUTSIDE of that 120 degrees will create a cord that is GREATER than 2. So, 240 degrees of the circle will give you the result that you're looking for.
Final answer: [spoiler]240/360 = 2/3 = D[/spoiler]
GMAT assassins aren't born, they're made,
Rich
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Question rephrased: Once A has been placed on the circle, what is the probability that B can be placed on the circle such that AB>2?guerrero wrote:If points A and B are randomly placed on the circumference of a circle with radius 2, what is the probability that the length of chord AB is greater than 2?
A)1/4
B)1/3
C)1/2
D)2/3
E)3/4
AB=2 if B is placed to the left or right of A as shown by B� and B₂ in the figure above.
If either B� or B₂ moves CLOSER to A, then AB<2.
Implication:
Since ∠B�OB₂ = 60+60 = 120º, and 120/360 = 1/3, AB≤2 for 1/3 of the circle.
Thus, AB>2 for the remaining 2/3 of the circle.
Resulting probability:
P(AB>2) = 2/3.
The correct answer is D.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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